Regularity Results for Nonlocal Equations by Approximation

Archive for Rational Mechanics and Analysis

Volumn 200, Issue 1, 2011, Pages 59-88

  Caffarelli, Luis ^a   Silvestre, Luis ^b  

^a UNIVERSITY OF TEXAS AT AUSTIN   (United States)

^b UNIVERSITY OF CHICAGO   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 79952706153     PISSN: 00039527     EISSN: 14320673     Source Type: Journal    
DOI: 10.1007/s00205-010-0336-4     Document Type: Article

References (9)

1. Barles, G., Chasseigne, E., Imbert, C.: Hölder continuity of solutions of second-order non-linear elliptic integro-differential equations. J. Eur. Math. Soc. (to appear).
2. Caffarelli L., Silvestre L.: Regularity theory for fully nonlinear integro-differential equations. Commun. Pure Appl. Math. 62(5), 597-638 (2009).
3. Caffarelli L. A.: Interior a priori estimates for solutions of fully nonlinear equations. Ann. of Math. (2) 130(1), 189-213 (1989).
4. Caffarelli, L. A., Cabré, X.: Fully Nonlinear Elliptic Equations. American Mathematical Society Colloquium Publications, Vol. 43. American Mathematical Society, Providence, RI, 1995.
5. Cordes H. O.: Über die erste Randwertaufgabe bei quasilinearen Differentialgleichungen zweiter Ordnung in mehr als zwei Variablen. Math. Ann. 131, 278-312 (1956).
6. Kassmann M.: A priori estimates for integro-differential operators with measurable kernels. Calc. Var. Partial Differ. Equ. 34(1), 1-21 (2009).
7. Mikulyavichyus R., Pragarauskas G.: Nonlinear potentials of the Cauchy-Dirichlet problem for the Bellman integro-differential equation. Liet. Mat. Rink. 36(2), 178-218 (1996).
8. Nirenberg, L.: On a generalization of quasi-conformal mappings and its application to elliptic partial differential equations. In Contributions to the Theory of Partial Differential Equations. Annals of Mathematics Studies, Vol. 33. Princeton University Press, Princeton, 95-100, 1954.
9. Silvestre L.: Hölder estimates for solutions of integro-differential equations like the fractional laplace. Indiana Univ. Math. J. 55(3), 1155-1174 (2006).